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On semiparametric familial-longitudinal models

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  • Sneddon, Gary
  • Sutradhar, Brajendra C.

Abstract

The familial-longitudinal data are collected from a large number of groups or families over a small period of time. This type of data exhibit two-way correlations. First, the responses of the members of a family are likely to be correlated. Second, when the familial responses are repeatedly collected over time, they also exhibit longitudinal correlations. In this paper, we propose a semiparametric linear model with a two-way correlated error structure that accommodates both the longitudinal and familial correlations. We use the generalized least squares method for the estimation of the parametric regression function, whereas the time trend function is estimated by a locally weighted regression smoother. The longitudinal and familial correlations are estimated by using the method of moments. The performance of the estimation methodology is examined through a simulation study by generating the errors of the linear model from multivariate normal as well as heavy-tailed t-distributions. The estimators appear to perform quite well in estimating their parametric and nonparametric population counterparts, including the longitudinal and familial correlations.

Suggested Citation

  • Sneddon, Gary & Sutradhar, Brajendra C., 2004. "On semiparametric familial-longitudinal models," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 369-379, September.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:3:p:369-379
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    References listed on IDEAS

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    1. Schick, Anton, 1996. "Efficient estimation in a semiparametric additive regression model with autoregressive errors," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 339-361, February.
    2. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
    3. Anton Schick, 1998. "An Adaptive Estimator of the Autocorrelation Coefficient in Regression Models with Autoregressive Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(5), pages 575-589, September.
    4. Vandna Jowaheer, 2002. "Analysing longitudinal count data with overdispersion," Biometrika, Biometrika Trust, vol. 89(2), pages 389-399, June.
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    1. Nan Zheng & Brajendra C. Sutradhar, 2018. "Inferences in semi-parametric dynamic mixed models for longitudinal count data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 215-247, February.
    2. Brajendra C. Sutradhar, 2018. "Semi-parametric Dynamic Models for Longitudinal Ordinal Categorical Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 80-109, February.
    3. Brajendra C. Sutradhar & R. Prabhakar Rao, 2023. "Asymptotic Inferences in a Doubly-Semi-Parametric Linear Longitudinal Mixed Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 214-247, February.

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